A bag contains eight counters that are red, blue or yellow. A counter is selected from the bag, its colour noted and the counter replaced. If 100 counters were selected and 14 were red, 37 were blue and 49 were yellow, how many counters of each colour are likely to be in the bag?
14% are red, 37% blue, 49% yellow in our samples.
so of 8 approximately:
1.12 red
2.96 blue
3.92 yellow
luckily 1 + 3 + 4 = 8
To solve this problem, we can set up a proportion using the information given.
Let's represent the number of red counters in the bag as 'x', the number of blue counters as 'y', and the number of yellow counters as 'z'.
We are given that 14 out of 100 counters were red, which can be written as:
({number of red counters}) / ({total number of counters}) = 14 / 100
From this, we can set up the proportion:
(x / 100) = (14 / 100)
Simplifying the proportion, we have:
x = (14 * 100) / 100
x = 1400 / 100
x = 14
Therefore, there are likely 14 red counters in the bag.
Similarly, we can set up the proportions for blue and yellow counters:
(y / 100) = 37 / 100
y = (37 * 100) / 100
y = 37
Therefore, there are likely 37 blue counters in the bag.
(z / 100) = 49 / 100
z = (49 * 100) / 100
z = 49
Therefore, there are likely 49 yellow counters in the bag.
In conclusion, based on the information provided and using proportions, there are likely 14 red counters, 37 blue counters, and 49 yellow counters in the bag.
To determine how many counters of each color are likely to be in the bag, we can use a statistical approach.
First, let's find the probability of selecting each color. We'll calculate the probability for each color using the formula:
Probability = Number of occurrences / Total number of counters
The probability of selecting a red counter is 14/100 = 0.14 (or 14%).
The probability of selecting a blue counter is 37/100 = 0.37 (or 37%).
The probability of selecting a yellow counter is 49/100 = 0.49 (or 49%).
Now, let's assume that the number of each color counter in the bag is proportional to the probability of selecting that color. We'll assign variables to represent the number of each color:
Let R be the number of red counters.
Let B be the number of blue counters.
Let Y be the number of yellow counters.
Since we assume that the number of each color counter in the bag is proportional to the probability of selecting that color, we have the following relationships:
R/100 = 0.14
B/100 = 0.37
Y/100 = 0.49
To find the values of R, B, and Y, we can cross-multiply and solve for each variable:
R = 0.14 * 100 = 14
B = 0.37 * 100 = 37
Y = 0.49 * 100 = 49
Therefore, based on the given information, there are likely 14 red counters, 37 blue counters, and 49 yellow counters in the bag.